Cognitive framework for blended mathematical sensemaking in science

Abstract

Background: Blended mathematical sensemaking in science (“Math-Sci sensemaking”) involves deep conceptual understanding of quantitative relationships describing scientific phenomena and has been studied in various disciplines. However, no unified characterization of blended Math-Sci sensemaking exists. Results: We developed a theoretical cognitive model for blended Math-Sci sensemaking grounded in prior work. The model contains three broad levels representing increasingly sophisticated ways of engaging in blended Math-Sci sensemaking: (1) developing qualitative relationships among relevant variables in mathematical equations describing a phenomenon (“qualitative level”); (2) developing mathematical relationships among these variables (“quantitative level”); and (3) explaining how the mathematical operations used in the formula relate to the phenomenon (“conceptual level”). Each level contains three sublevels. We used PhET simulations to design dynamic assessment scenarios in various disciplines to test the model. We used these assessments to interview undergraduate students with a wide range of Math skills. Interview analysis provided validity evidence for the categories and preliminary evidence for the ordering of the categories comprising the cognitive model. It also revealed that students tend to perform at the same level across different disciplinary contexts, suggesting that blended Math-Sci sensemaking is a distinct cognitive construct, independent of specific disciplinary context. Conclusion: This paper presents a first-ever published validated cognitive model describing proficiency in blended Math-Sci sensemaking which can guide instruction, curriculum, and assessment development.